Yuto is correct because he isolated the variable correctly and reversed the inequality symbol.
x < 3
<span>ΔABC is not a right triangle.</span>
Answer:0.816
Step-by-step explanation:
Ape x
Answer:
The solution set is {4, -1}
Step-by-step explanation:
6x²- 18x -18 = 6
6x²- 18x -18 - 6 = 0
6x²- 18x -24 = 0
6(x² - 3x - 4) = 0
6(x - 4)(x + 1) = 0
6 = 0 not true
x - 4 = 0 ; x + 1 = 0
x = 4 x = - 1
The solution set is {4, -1}
(a) x = 4
First, let's calculate the area of the path as a function of x. You have two paths, one of them is 8 ft long by x ft wide, the other is 16 ft long by x ft wide. Let's express that as an equation to start with.
A = 8x + 16x
A = 24x
But the two paths overlap, so the actual area covered will smaller. The area of overlap is a square that's x ft by x ft. And the above equation counts that area twice. So let's modify the equation by subtracting x^2. So:
A = 24x - x^2
Now since we want to cover 80 square feet, let's set A to 80. 80 = 24x - x^2
Finally, let's make this into a regular quadratic equation and find the roots.
80 = 24x - x^2
0 = 24x - x^2 - 80
-x^2 + 24x - 80 = 0
Using the quadratic formula, you can easily determine the roots to be x = 4, or x = 20.
Of those two possible solutions, only the x=4 value is reasonable for the desired objective.
(b) There were 2 possible roots, being 4 and 20. Both of those values, when substituted into the formula 24x - x^2, return a value of 80. But the idea of a path being 20 feet wide is rather silly given the constraints of the plot of land being only 8 ft by 16 ft. So the width of the path has to be less than 8 ft (the length of the smallest dimension of the plot of land). Therefore the value of 4 is the most appropriate.
